Fuzzy multiobjective differential evolution stopping criteria based on performance metrics feedback

Abstract

Differential evolution is one of the most efficient optimization algorithms for solving complication problems including single objective, multiobjective and many-objective optimization. It is a stochastic population-based search approach for optimization over the continuous space. The main advantages of differential evolution are simplicity, robustness and high speed of convergence. The Advanced Fuzzy-based Multiobjective Differential Evolution (AFMDE) that exploits three performance metrics, specifically hypervolume, spacing, and maximum spread, to measure the state of the evolution process. The fuzzy inference rules are applied to these metrics in order to adaptively adjust the associated control parameters of the chosen mutation strategy used in AFMDE. The optimization algorithm will stop the evolution process if the number of iterations reaches the stopping criteria which usually is the maximum number of iterations. Then, the optimization algorithm delivers the optimal solution founded. However, sometimes if the maximum number of iterations is not appropriately defined, the found solutions may not be the optimal ones. In case of the optimization algorithm has found the optimal solutions but it must continue the evolution process because the stopping criteria are not met. This can cause unnecessary using of high computational resources and time-consuming. Therefore, this research study proposed the stopping criteria based on performance metrics feedback for AFMDE. The efficiency of the proposed criteria combined with AFMDE is evaluated on the well-known ZDT benchmark test suites.